Septic B-spline method for solving nonlinear singular boundary value problems arising in physiological models

Hadhoud, Adel R.; Ali, Khalid K.; Shaalan, M.A.

doi:10.24200/sci.2018.51012.1961

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…The optimal homotopy analysis procedure was applied to the model (1) in [15]. The technique of the B-Spline collocation scheme was employed in [16]. A hybrid method based on the modified ADM and quintic B-spline collocation strategy was given in [17].…”

Section: Introductionmentioning

confidence: 99%

The Reaction–Diffusion Models in Biomedicine: Highly Accurate Calculations via a Hybrid Matrix Collocation Algorithm

Izadi,

Srivastava

2023

Applied Sciences

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A hybrid efficient and highly accurate spectral matrix technique is adapted for numerical treatments of a class of two-pint boundary value problems (BVPs) with singularity and strong nonlinearity. The underlying model is a reaction-diffusion equation arising in the modeling of biomedical, chemical, and physical applications based on the assumptions of Michaelis–Menten kinetics for enzymatic reactions. The manuscript presents a highly computational spectral collocation algorithm for the model combined with the quasilinearization method (QLM) to make the proposed technique more efficient than the corresponding direct spectral collocation algorithm. A novel class of polynomials introduced by S.K. Chatterjea is used in the spectral method. A detailed proof of the convergence analysis of the Chatterjea polynomials (ChPs) is given in the L2 norm. Different numerical examples for substrate concentrations with all values of parameters are performed for the case of planar and spherical shapes of enzymes. For validation, these results are compared with those obtained via wavelet-based procedures and the Adomian decomposition scheme. To further improve the approximate solutions obtained by the QLM–ChPs method, the technique of error correction is introduced and applied based on the concept of residual error function. Overall, the presented results with exponential convergence indicate that the QLM–ChPs algorithm is simple and flexible enough to be applicable in solving many similar problems in science and engineering.

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Section: Introductionmentioning

confidence: 99%

The Reaction–Diffusion Models in Biomedicine: Highly Accurate Calculations via a Hybrid Matrix Collocation Algorithm

Izadi,

Srivastava

2023

Applied Sciences

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“…To the best of our knowledge, the present method has not been discussed in the numerical analysis literature for the solution of the problem under consideration. The numerical method based on B‐spline collocation method has been successfully applied to solve a wide variety of boundary value problem 39‐42 …”

Section: Introductionmentioning

confidence: 99%

An efficient numerical method based on exponential B‐spline basis functions for solving a class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions

Roul

Kumari

Goura

2020

Math Methods in App Sciences

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In this paper, we develop a numerical scheme to approximate the solution of a general class of nonlinear singular boundary value problems (SBVPs) subject to Neumann and Robin boundary conditions. The original differential equation has a singularity at the point x=0, which is removed via L'Hospital's law with an assumption about the derivative of the solution at the point x=0. An exponential B‐spline collocation approach is then constructed to solve the resulting boundary value problem. Convergence analysis of the method is discussed. Numerical examples are provided to illustrate the applicability and efficiency of the method. Our results are compared with those obtained by other three numerical methods such as uniform mesh cubic B‐spline collocation (UCS) method, nonstandard finite difference method, and finite difference method based on Chawla's identity.

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Septic B-spline method for solving nonlinear singular boundary value problems arising in physiological models

Cited by 2 publications

References 22 publications

The Reaction–Diffusion Models in Biomedicine: Highly Accurate Calculations via a Hybrid Matrix Collocation Algorithm

The Reaction–Diffusion Models in Biomedicine: Highly Accurate Calculations via a Hybrid Matrix Collocation Algorithm

An efficient numerical method based on exponential B‐spline basis functions for solving a class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions

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